Average Error: 0.0 → 0.0
Time: 13.5s
Precision: 64
Internal Precision: 320
\[\sqrt{1 - {\left(\frac{x}{{2}^{n}}\right)}^{2}}\]
\[\sqrt{1 - \frac{x}{{2}^{n}} \cdot \frac{x}{{2}^{n}}}\]

Error

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Bits error versus n

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Results

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Derivation

  1. Initial program 0.0

    \[\sqrt{1 - {\left(\frac{x}{{2}^{n}}\right)}^{2}}\]
  2. Initial simplification0.0

    \[\leadsto \sqrt{1 - \frac{x}{{2}^{n}} \cdot \frac{x}{{2}^{n}}}\]
  3. Final simplification0.0

    \[\leadsto \sqrt{1 - \frac{x}{{2}^{n}} \cdot \frac{x}{{2}^{n}}}\]

Runtime

Time bar (total: 13.5s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x n)
  :name "sqrt(1-(x/2^n)^2)"
  (sqrt (- 1 (pow (/ x (pow 2 n)) 2))))